Bäcklund Transformations and Exact Soliton Solutions for Some Nonlinear Evolution Equations of the zs/akns System

The general form of the Bäcklund transformations (BTs) for some nonlinear evolution equations (NLEEs) solvable by the inverse scattering method of Zakharov-Shabat/Ablowitz-Kaup-Newell-Segur (ZS/AKNS) and the ZS/AKNS wave functions corresponding to the soliton solutions of these NLEEs are considered. The method of characteristics is used and BTs are employed to generate new solutions from the old. Thus, families of new solution classes for the KdV equation, the mKdV equation, the sinh-Poisson equation, the Liouville equation, the stable nonlinear Schrödinger equation, the unstable nonlinear Schrödinger equation, and the inhomogeneous nonlinear Schrödinger equation are obtained.